Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect

TL;DR

This paper explores how superconducting proximity effects induce topological phase transitions in quantum anomalous Hall systems, leading to the emergence of non-abelian anyons and Majorana fermions with potential applications in quantum computing.

Contribution

It demonstrates the transformation of quantum anomalous Hall states into topological superfluids with non-abelian anyons via proximity effects, revealing new pathways for topological quantum computation.

Findings

Charge e/2 abelian anyons with neutral fermion zero modes

Emergence of Majorana fermions at edges during phase transitions

Superconducting proximity can induce non-abelian vortex excitations

Abstract

We study the quantum anomalous Hall effect described by a class of two-component Haldane models on square lattices. We show that the latter can be transformed into a pseudospin triplet p+ip-wave paired superfluid. In the long wave length limit, the ground state wave function is described by Halperin's (1,1,-1) state of neutral fermions analogous to the double layer quantum Hall effect. The vortex excitations are charge e/2 abelian anyons which carry a neutral Dirac fermion zero mode. The superconducting proximity effect induces `tunneling' between `layers' which leads to topological phase transitions whereby the Dirac fermion zero mode fractionalizes and Majorana fermions emerge in the edge states. The charge e/2 vortex excitation carrying a Majorana zero mode is a non-abelian anyon. The proximity effect can also drive a conventional insulator into a quantum anomalous Hall effect state with a Majorana edge mode and the non-abelian vortex excitations.